lecture 02 -- genotypes, phenotypes and hardy weinberg...
TRANSCRIPT
![Page 1: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/1.jpg)
Genotypes, Phenotypes and Hardy Weinberg Equilibrium
Biostatistics 666Lecture II
![Page 2: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/2.jpg)
Previously: Refresher on Genetics
� DNA sequence� Human Genome
� Inheritance of genetic information � Sequence variation
� VNTRs, microsatellites and SNPs
� Common Types of Genetic Study
![Page 3: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/3.jpg)
Gregor Johann Mendel� Discovered basic principles of genetics
� “The Father of Genetics”� Monk, lived 1822 – 1884
� Crosses between strains of peas� Garden pea (Pisum sativum)� Each strain has particular characters� Height, flower color, seed shape …
![Page 4: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/4.jpg)
Mendel’s Experiment� Crossed different true-
breeding strains� Identical results for
reciprocal crosses
� F1 resembled one of the parental strains
� In F2 generation, the other parental trait reappears …
![Page 5: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/5.jpg)
Mendel’s Numbers� Seeds: Yellow vs. Green
� F1: All yellow� F2: 6022 yellow, 2001 green
� 75.1% yellow, 24.9% green
� Seeds: Smooth vs. Wrinkled� F1: All smooth� F2: 5474 smooth, 1850 wrinkled
� 74.7% yellow, 25.3% wrinkled
![Page 6: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/6.jpg)
Phenotype vs. Genotype� Genotype
� Underlying genetic constitution
� Phenotype� Observed manifestation of a phenotype
� The yellow peas in the parental and F1generations are not the same
![Page 7: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/7.jpg)
Mendel’s Interpretation� Each trait determined by “particulate factors”
(genes)� E.g.: Seed colour
� Alternative forms for each factor (alleles)� E.g.: Yellow seeds or green seeds
� Each plant carried two alleles� Identical for true breeding parental strains� Different for F1 generation
![Page 8: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/8.jpg)
The Principle of Segregation� Mendel’s First Law� The two alleles of a gene pair segregate
from each other in the formation of gametes
(gametes are reproductive cells that fuse to form a new organism in sexual reproduction)
![Page 9: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/9.jpg)
Genotypes� Each individual carries two alleles
� If there are n alternative alleles … � … there will be n(n+1)/2 possible genotypes
� Homozygotes� The two alleles are the same� E.g.: Green/Green or Yellow/Yellow
� Heterozygotes� The two alleles are different� E.g.: Green/Yellow
![Page 10: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/10.jpg)
Penetrance� Describes the relationship between
phenotypes and genotypes� Complete Penetrance
� Each genotype corresponds to only one phenotype
� Incomplete Penetrance� Link between phenotype and genotype is only
probabilistic
![Page 11: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/11.jpg)
The ABO blood group� Important for blood transfusions� Determined by alleles of the ABO gene� 3 alternative alleles
� A, B and O
� 6 possible genotypes, n (n + 1) / 2� A/A, A/B, A/O, B/B, B/O, O/O
![Page 12: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/12.jpg)
ABO Blood Group II
A B A BA + - - +B - + + -O - - + +AB + + - -
Antigen AntibodyPhenotype
![Page 13: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/13.jpg)
Relationships between alleles� Relation between alleles
� A and B are dominant over O
� O is recessive in relation to A and B
� A and B are codominant
� In this case all genotypes are fully penetrant
Genotype PhenotypeA/A AA/B ABA/O AB/B BB/O BO/O O
![Page 14: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/14.jpg)
BRCA1 and Breast Cancer� BRCA1 mutations predispose to breast
cancer� About 0.1% of the population carries
mutations in the BRCA1 gene� Disease Risk
� Age 40 60 80� Carriers 40% 70% 80%� Non-carriers 0.4% 3% 8%
![Page 15: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/15.jpg)
Alleles, Genotypes and Phenotypes
� Classifying genotypes� Homozygous� Heterozygous
� Penetrance� Relationships between alleles
� Dominant, Recessive, Co-Dominant
![Page 16: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/16.jpg)
Genes in Populations� Genotype Frequencies� Haplotype Frequencies� Allele Frequencies� Penetrance Function
� Derived measures of marker informativeness
![Page 17: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/17.jpg)
Notation
� pij� frequency of genotype i/j in the population� n(n+1)/2 of these
� pi� frequency of allele i in the gene pool� n of these
� Write allele frequencies as function of genotype frequencies
![Page 18: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/18.jpg)
Hardy-Weinberg Equilibrium� Random union of games� Relationship discovered it in 1908
� Hardy, British mathematician� Weinberg, German physician
� Shows n allele frequencies determine n(n+1)/2 genotype frequencies� Large populations
![Page 19: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/19.jpg)
Required Assumptions� Diploid, sexual organism
� Non-overlapping generations� Autosome� Large population� Random mating� Equal genotype frequencies among
sexes� Selection
![Page 20: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/20.jpg)
Random Mating:Mating Type Frequencies
Mating FrequencyA1A1*A1A1 p11²A1A1*A1A2 2p11p12A1A1*A2A2 2p11p22A1A2*A1A2 p12²A1A2*A2A2 2p12p22A2A2*A2A2 p22²Total 1.0
![Page 21: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/21.jpg)
Mendelian Segregation:Offspring Genotype Frequencies
Mating Frequency A1A1 A1A2 A2A2A1A1*A1A1 p11² p11²A1A1*A1A2 2p11p12 p11p12 p11p12A1A1*A2A2 2p11p22 2p11p22A1A2*A1A2 p12² ¼p12² ½p12² ¼p12²A1A2*A2A2 2p12p22 p12p22 p12p22A2A2*A2A2 p22² p22²
Offspring
![Page 22: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/22.jpg)
And now…
21
1221
221221
11
2122
122121211221112
22
2122
122
2124
11222
22222
21
2122
111
2124
11211
21111
2))((2
2'
)('
)('
pppppp
ppppppppp
ppppppp
ppp
ppppp
�
���
����
�
��
���
�
��
���
![Page 23: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/23.jpg)
Conclusion� Genotype frequencies are function of
allele frequencies� Equilibrium reached in one generation� Independent of initial genotype frequencies� Random mating, etc. required
� Conform to binomial expansion� (p1 + p2)2
= p12 + 2p1p2 + p2
2
![Page 24: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/24.jpg)
A few more notes…� Can be expanded to multiple alleles
� Expand (p1 + p2 + p3 + · · · + pk)2
� Holds in almost all human populations� Little inbreeding (typical F = ~0.005)
� Deviations can suggest:� Problems with experimental assays� Non-independence of observations� Selection� Disease locus
![Page 25: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/25.jpg)
Heterozigosity� Probability that two alleles will differ
� For a equally frequent alleles
� Sometimes called “gene diversity”
���21 ipH
aa
aH 111
�
���
![Page 26: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/26.jpg)
PIC� Probability that alleles of parent can be
distinguished in offspring� Botstein et al, 1980.
� Markers that could track dominant alleles
� Probability that parent will heterozygous and informative in relation to spouse
![Page 27: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/27.jpg)
PIC – Definition� In general:
� For a equally frequent alleles
� PIC <= H
� � �� � ��
���
n
i
n
i
n
ijjii pppPIC
1 1 1
22 )(21
3
11aa
aaPIC
�
�
�
�
![Page 28: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/28.jpg)
Exercise� ABO locus allele frequencies
� A – frequency 0.3� B – frequency 0.1� O – frequency 0.6
� Calculate genotype frequencies� Calculate heterozygosity and PIC� Calculate phenotype frequencies
![Page 29: Lecture 02 -- Genotypes, Phenotypes and Hardy Weinberg ...csg.sph.umich.edu/abecasis/class/2003/Lecture02.pdfGenotype frequencies are function of allele frequencies Equilibrium reached](https://reader033.vdocuments.us/reader033/viewer/2022050102/5f416a6e35c3506d3031c0c2/html5/thumbnails/29.jpg)
NOD2 and Bowel Disease� Leu1007fs
� Frame shift mutation at position 1007� Frequency of about 5%� Disrupts gene
� Penetrance� Genotype +/+ -/+ -/-� P(Crohn’s|G) 0.1% 0.2% 3%
� Calculate frequency of -/- genotype in population and among patients…